Following [1]}, an element \(w\)  of a ring \(R\)  is said to be clean if \(w\)  is a sum of a unit, and an idempotent of \(R\) , \(w\)  is said to be exchange if there exist \(e\in E(R)\)  such that \(e\in wR\)  and \(1-e\in (1-w)R\) . \(R\)  is said to be clean if every element of \(R\)  is clean, and \(R\)  is said to be exchange if every element of \(R\)  is exchange. It is well known that clean rings are exchange.
